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AMO 2021 - Primary 5 (Grade 5)

Question 1

There are three numbers $A$, $B$, and $C$. $B$ is one-third more than $A$, and $C$ is one-fourth less than $B$. Which statement is true?

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  1. A is three-fourths of C
  2. A is the same as C
  3. C is four-thirds of A
  4. A is one-twelfth of C
  5. C is one-seventh of A

Question 2

Letter blocks form a rectangle 18 blocks long and 8 blocks wide. If all the blocks are rearranged into a square, how many blocks wide is the square?

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  1. 36
  2. 25
  3. 8
  4. 12
  5. 64

Question 3

Three-sevenths of a number is 60. What is two-fifths of that number?

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  1. 65
  2. 78
  3. 56
  4. 24
  5. 37

Question 4

Harvey colors a growing pattern of small hexagons, starting at the upper left with one hexagon, then three, and so on. The picture shows five completed steps. After completing the sixth step, how many hexagons will he have colored in total?

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  1. 24
  2. 30
  3. 32
  4. 36
  5. 64

Question 5

What is the product of all natural numbers that divide evenly into 10? Here natural numbers are whole numbers; 0 is not a divisor.

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  1. 100
  2. 60
  3. 120
  4. 50
  5. 48

Question 6

How many triangles of all sizes are in the figure?

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  1. 5
  2. 7
  3. 8
  4. 4
  5. 6

Question 7

Katie has 5 different shirts, 6 different skirts, 5 different hats, and 4 different pairs of shoes. How many outfits can she make by choosing one of each?

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  1. 50
  2. 5654
  3. 20
  4. 600
  5. 60

Question 8

Jake surveyed all his classmates about their favorite fruit and made the chart. What percentage of his classmates chose apples?

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  1. 18%
  2. 36%
  3. 60%
  4. 75%
  5. 80%

Question 9

Linda uses a four-digit smartphone passcode. Each position can contain any digit from $\{0,1,2,3,4,5,6,7,8,9\}$. How many passcodes are possible? Repeated digits and an initial 0 are allowed.

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  1. 1000
  2. 40
  3. 10000
  4. 100
  5. 400

Question 10

The average of three numbers is 16. Replacing one number by 4 changes the average to 10. What was the original value of the replaced number?

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  1. 78
  2. 40
  3. 22
  4. 20
  5. 26

Question 11

John says, “If you triple my age and add 5, you get 38.” How old is John?

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  1. 21
  2. 12
  3. 11
  4. 10
  5. 13

Question 12

Matt’s fish tank initially contains 1 gallon of water. Each month it loses three-tenths of its water, and Matt cannot refill it. After how many months has it lost more than half of its initial water? A gallon is a unit of liquid capacity. Interpret each monthly loss as three-tenths of the water remaining.

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  1. One month
  2. Two months
  3. Three months
  4. Four months
  5. Five months

Question 13

Two natural numbers greater than 1 have product 65. What is their sum?

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  1. 12
  2. 15
  3. 16
  4. 18
  5. 20

Question 14

Bill uses each of the digits 7, 2, and 5 exactly once to form a three-digit number. What is the difference between the largest and smallest numbers he can make?

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  1. 450
  2. 495
  3. 512
  4. 252
  5. 315

Question 15

Hailey makes paper stars at a rate of 2 stars per hour. Which labeled point represents the number of stars she has made after 3 hours?

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  1. G
  2. H
  3. I
  4. J
  5. K

Question 16

Find the sum of all whole numbers between 1 and 100 that are multiples of 3.

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Question 18

An online store reduced the price of a toy car by 25%, so it sold for 24 dollars. What was the original price, in dollars?

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Question 19

The two gears in the figure turn together. When the small gear has made 60 turns, how many turns has the large gear made?

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Question 20

A turtle is at $(2,-5)$ and a worm is at $(5,6)$ in the coordinate plane. The turtle moves one unit horizontally or vertically per step. What is the minimum number of steps needed to reach the worm?

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